Hi there. In this math guide, I cover the area of a circle sector. For the screenshots I use the Math Is Fun online whiteboard and witeboard.com.
Before getting into the area of a circle sector it is good to review the area of a circle. Given the radius of the circle r, the area of the circle is given by Area = πr².
If you are given the diameter of the circle, talk half the length of the diameter (d) to obtain the circle's radius.
The sector of a circle refers to the part of the circle given an angle from 0 degrees to 360 degrees. In radians, the angle is from 0 to 2π. (π is pi) Picture taken from https://byjus.com/maths/area-of-sector/.
For the area of the circle, the formula is given by the area of the circle multiplied by the fraction of the angle divided by a full rotation of 360 degrees (or 2π). The symbol θ (theta) is used to represent the angle for the sector of a circle.
Note that Pi (π) radians is equal to 180 in degrees.
Example One
Given an angle of 30 degrees in a circle and a radius of 8 centimetres, what is the area of the orange sector of the circle?
Example Two
A circle has a radius of 10 metres and an angle of π/4 radians, what is the area of the sector of the circle?
Example Three
The area of the sector of the circle is 3π/2 square units. This circle has a radius of 3 units. What is the angle of the circle sector?
Thank you for reading.
